Bonferroni's Method for Pairwise Multiple Comparisons

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The Bonferroni method is a post-hoc procedure conducted after an ANOVA test or Kruskal-Wallis test whenever the null hypothesis has been rejected and have concluded a significant difference in at least 2 means. It is a pairwise comparison that distinguishes which groups are significantly different.

Bonferroni uses confidence intervals to conclude a significant difference. The interval is calculated using the formula below:

Where B=Z_((1−α/2g) ) and g is the number of pairwise comparisons of interest (usually all pairwise comparisons are investigated). g is calculated by g=k(k−1)/2.

Q. Using the same example we used in our previous lesson,

Based on the Kruskal-Wallis test, we concluded that at least two treatment group means differed @ 0.05 significance level.

Use the Bonferroni method to calculate confidence intervals for all the pairwise differences between the treatments. Use the 95% confidence level to find out which ones are significantly different.